Steve,
I learned a fairly expensive avionics lesson a few months ago: My autopilot was not connecting...and when it would, it would just disconnect with no notice. After considerable work by the avionics shop, including sending mine back to the manufacturer, they found nothing wrong. Eventually, the shop discovered it was a broken (or shorted) wire in the yoke, connecting the disconnect switch to the A/P brain unit. It took maybe 30 minutes to fix after that was determined. Been working great since then....
A similar thing happened to me a couple years ago when I was on the way to Sun n Fun: ADI froze up and would not work. After a week's trouble-shooting, and some new parts, they (a different shop) discovered just a broken wire behind the instrument panel.
Oh well...
Ed